The Jets made their final cuts this weekend and there was one particular player who, for a deserved change, didn’t have to endure a nervous night of tossing and turning in bed wondering about his fate with the Turk looming.

That player was Jets receiver Kevin Swayne, one of the true feel-good stories of the NFL.

A year ago, Swayne had little idea which direction his life was headed. And, perhaps making matters even more stressful, he was too tired to think too much about it.

Swayne, who with a solid training camp has solidified his position as the Jets’ No. 4 receiver as they get set to begin this week in preparation for the regular-season opener against the Bills in Buffalo, came to the Jets last year as a wing-and-a-prayer longshot to merely make the final roster. He was coming off consecutive seasons in the now-defunct XFL and the Arena League and was signed by the Jets when Santana Moss suffered a knee-cartilage injury.

Despite having played two consecutive full seasons in other football leagues, Swayne somehow survived training camp, made the team and even contributed in some key spots.

A year later, he feels like a new man with an offseason of rest and a secure job. Now that the quietly, classy Swayne has a secure job, though, doesn’t mean he’s going to coast. There isn’t a complacent bone in his body.

“You always have to have that fighting mentality,” Swayne said. “If I don’t go about it like that then I’m letting the team down, because that’s what allowed me to make it last year. I’m not just satisfied being a No. 4 receiver. I don’t try to think about what I accomplished last year. I’m focused on the next day.

“I am so much more relaxed, though, because it’s a humongous difference to completely feel comfortable with the speed of the game, which is so much different,” he went on. “Every catch in this league is a tight catch. Here, a routine catch is a great catch.”

Swayne caught 13 passes for a 15.6-yard average last season. His best game came against the Bengals when he caught four passes for 74 yards; all four catches came on third downs and went for first downs. He, too, made some clutch grabs against the Steelers in Pittsburgh.

“It didn’t prove anything to myself, but it was an opportunity to go out there and finally do it on the field,” Swayne said. “When you get that opportunity, you’ve got take advantage of it. It let the rest of the team know, ‘That’s why this kid is here. ‘ It was good to get that out of the way.”

Swayne has continued to make progress this summer, looking stronger and surer of himself. A week ago, he caught a TD pass from Chad Pennington against the Giants in tight coverage. It seemed as if every one of those opportunities slipped tantalizingly off his fingertips last year.

That wasn’t lost on Pennington, who was delighted to get Swayne into the end zone for the first time as an NFL player.

“He’s worked so hard and been through a lot over the past year, so that was very satisfying to get him a touchdown,” Pennington said. “Kevin just tries to do things right. That’s his best quality. You don’t get any excuses out of him. No complaints. You just get good hard work and a great attitude. That’s why he’s been successful.”

“That’s my job; I’m supposed to score touchdowns,” Swayne said before adding, “I wasn’t going to keep the football or anything,” and then admitting, “That allowed me to exhale so I can go on and catch more of those.”

Swayne called being an established part of the Jets “a different feeling” than he’s ever had, “because I can have the peace of mind of being able to just concentrate on football.”

Earlier in training camp there was a telling moment as to just how difficult a road Swayne had traveled to make it as a Jet.

Free-agent hopeful receiver Mike Furrey, who like Swayne had a year ago, was coming off a season with the Arena League’s New York Dragons and trying to make the Jets. It took only several days of two-a-day practices before Furrey told Herman Edwards his body and mind were too tired to continue, and so he retired despite much encouragement from Swayne.

“He’d asked me a number of times, ‘How do you do this?’ ” Swayne said of Furrey. “I just said, ‘By the grace of God.’ ”